PRIN.OF HIGHWAY ENGINEERING&TRAFFIC ANA.
7th Edition
ISBN: 9781119610526
Author: Mannering
Publisher: WILEY
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Chapter 8, Problem 29P
To determine
The user equilibrium flows for the given condition.
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Students have asked these similar questions
3. Three routes connect an origin-destination pair with performance functions:
ti=20 +0.51
t₂ = 4+2x2
tε = 3 +0.2x²
with t in minutes and r in thousand vehicles per hour.
(a) Determine the User Equilibrium flow on each route if q = 4000veh/h.
(b) What is the minimum q (origin-destination demand) to ensure that all the three routes are used
under user equilibrium?
(c) Suppose that Route 1 is closed for repair. Find the system optimal flow on routes 2 and 3 and
compute the total travel times.
Suppose that the projected road vehicle traffic flow in a corridor is 5000 vehicle-trips per hour
in one direction. The average perceived user cost functions of the two major highways (Route
1 and Route 2 in the corridor are as follows (in dollars):
Route 1: Ci =1 +8(qı/5000)
Route 2: C2 = 1+10(q2/2500)
Where: qi and q2 are the traffic flows on Route 1 and Route 2 respectively.
Calculate the volume of traffic during the peak hour on each route, if users were free to
choose their own routes.
Example:
A busy travel corridor connecting a suburb with the city center is
served by two routes having a typical travel time function, t =a +
b(q/c), where t is the time in minutes, q is the vehicular flow in
veh/hr, and c is the capacity of the route in veh/hr. The existing
characteristics of the two routes is as follows:
Route a b c
1
34
3000
2
4 2 4000
(a) If the existing peak-hour demand is 5000 veh/hr, what is the traffic
distribution on the two routes?
(b) If repair work on Route 1 reduces its capacity to 2000 veh/hr, what
is likely to be the traffic distribution on the two routes for the
duration of the repairs?
(c) It is anticipated that after the repairs are completed on Route 1, its
capacity will be 4200 veh/hr. How will this affect the distribution.
Chapter 8 Solutions
PRIN.OF HIGHWAY ENGINEERING&TRAFFIC ANA.
Ch. 8 - Prob. 1PCh. 8 - Prob. 2PCh. 8 - Prob. 3PCh. 8 - Prob. 4PCh. 8 - Prob. 5PCh. 8 - Prob. 6PCh. 8 - Prob. 7PCh. 8 - Prob. 8PCh. 8 - Prob. 9PCh. 8 - Prob. 10P
Ch. 8 - Prob. 11PCh. 8 - Prob. 12PCh. 8 - Prob. 13PCh. 8 - Prob. 14PCh. 8 - Prob. 15PCh. 8 - Prob. 16PCh. 8 - Prob. 17PCh. 8 - Prob. 18PCh. 8 - Prob. 19PCh. 8 - Prob. 20PCh. 8 - Prob. 21PCh. 8 - Prob. 22PCh. 8 - Prob. 23PCh. 8 - Prob. 24PCh. 8 - Prob. 25PCh. 8 - Prob. 26PCh. 8 - Prob. 27PCh. 8 - Prob. 28PCh. 8 - Prob. 29PCh. 8 - Prob. 30PCh. 8 - Prob. 31PCh. 8 - Prob. 32PCh. 8 - Prob. 33PCh. 8 - Prob. 34PCh. 8 - Prob. 35PCh. 8 - Prob. 36PCh. 8 - Prob. 37PCh. 8 - Prob. 38PCh. 8 - Prob. 39P
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- Two routes connect an origin-destination pair with performance functions t₁ = 5 + (x₁/2)² and t₂ = 7+ (x2/4)² (with t's in minutes and x's in thousands of vehicles per hour). It is known that at user equilibrium, 75% of the origin-destination demand takes route 1. What percentage would take route 1 if a system-optimal solution were achieved, and how much travel time would be saved?arrow_forwardThree routes connect an origin-destination pair with performance functions:t₁ = 20 +0.5x1t2 = 4+ 2x2t3=3+0.2x3with t in minutes and x in thousand vehicles per hour.(a) Determine the User Equilibrium flow on each route if q = 4000veh/h. (b) What is the minimum q (origin-destination demand) to ensure that all the three routes are used under user equilibrium? (c) Suppose that Route 1 is closed for repair. Find the system optimal flow on routes 2 and 3 and compute the total travel times.arrow_forwardTwo routes connect an origin and destination with performance function t; = aj + (xj/cj)2 (with t's in minutes and x's in thousands of vehicles per hour). It is known that at user equilibrium, 65% of the origin-destination demand takes route 1. How many vehicles (in thousands) will take route 1 if system optimal equilibrium is archived? Route 1 Route 2 a 7 2 3arrow_forward
- Three routes connect an origin to a destination with the following link performance functions: t_1 = 8 + 0.5 x_2 t_2 = 1 + 2x_2 t_3 = 3 + 0.75x_3 where t's in minutes and x's in thousands of vehicle per hour. If the peak-hour traffic demand is 4000 vehicles, determine the user equilibrium (UE) flows.arrow_forwardEstimate the daily demand (DD) in (L/day) for a city of 5.2 x 106 persons, if average daily flow = Qave = 225 Lpcd, Maximum Daily Demand = Qmax =1.8 Qave: %3D Select one: O a. 117000000 L/day O b. 2270000000 L/day O c. 11700000 L/day O d. 1170000000 L/day Next page er (3) = Water Supply and Jump to... Water Treatment 2)arrow_forwardThe performance function for a highway connecting a suburb with the business district can be represented by a straight line of the form t = a + bq, where t is the travel time in minutes, q is the traffic flow in vehicles per hour, and a and b are constants equal to 15 minutes and 0.01 minute/vehicle-hour, respectively. The demand function, also represented by a straight line, is q = c - dt, where c and d are constants equal to 6000 vehicles/hr and 150 vehicles/hour/minute, respectively. (a) Find the equilibrium flow (q*) and the corresponding equilibrium time (t*) algebraically, and sketch the functions. (b) If the length of this highway is 25 miles, what is the average speed of vehicles along this highway? (c) It is proposed to improve this highway such that constant b is now 0.005. What would be the new values of t* and q* and what would be the average speed on this highway?arrow_forward
- 8.18 Two routes connect an origin and a destination. Routes 1 and 2 have performance functions t₁ = 2 + x₁ and t₂ = 1 + x2, where the 's are in minutes and the x's are in thousands of vehicles per hour. The travel times on the routes are known to be in user equilibrium. If an observation for route 1 finds that the gaps between 30% of the vehicles are less than 6 seconds, estimate the volume and average travel times for the two routes. (Hint: Assume a Poisson distribution of vehicle arrivals, as discussed in Chapter 5.)arrow_forwardQUESTION 1 A six-lane highway (3 lanes in each direction) is being designed to service a directional demand volume of 3,200 vehicles per hour. The PHF is expected to be 0.90. If the combination of trucks, buses, and recreational vehicles is represented by a heavy vehicle adjustment of 0.80, what is the flow rate (pcphpl)? Provide your answer to the nearest integer.arrow_forwardThe performance function for a highway connecting a suburb with the business district can be represented by a straight line of the form t = a + bp, where t is the travel time in minutes, q is the traffic flow in vehicles per hour, and a and b are constants equal to 15 minutes and 0.01 minute/vehicle-hour, respectively. The demand function, also represented by a straight line, is q = c + dt, where c and d are constants equal to 6000 vehicles/hr and vehicles/hour/minute, respectively. (a) Find the equilibrium flow (q*) and the corresponding equilibrium time (t*) algebraically, and sketch the functions. (b) If the length of this highway is 25 miles, what is the average speed of vehicles along this highway? (c) It is proposed to improve this highway such that constant b is now 0.005. What would be the new values of t* and q* and what would be the average speed on this highway?arrow_forward
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